Sensing of Low-Frequency Electric Fields Using Rydberg EIT within the Fisher Information Framework

Rydberg atoms, which possess exceptionally large electric dipole moments, offer a promising route for electric field sensing as well as metrology traceable to the International System of Units (SI); however, current research predominantly focuses on the microwave (MW) regime, leaving the quasi-direct current (quasi-DC) and low-frequency bands, ubiquitous in power systems, largely unexplored. In this paper, we present a theoretical investigation into low-frequency electric field detection. To this end, we establish a comprehensive modeling framework incorporating Fisher information (FI) and the Cram\'{e}r-Rao lower bound (CRLB) to quantify the fundamental precision limits of electromagnetically induced transparency (EIT) readouts. Building upon this framework, we propose a linearized sensing strategy utilizing a DC-biased two-point differential measurement. Numerical validations demonstrate that this approach effectively mitigates the weak-field insensitivity for both DC and AC fields, achieving a CRLB-limited sensitivity bound of approximately $1\times 10^{-4}$ V/m/$\sqrt{\text{Hz}}$. Furthermore, to surpass the single-pass sensitivity limit, we introduce a Fabry-P\'{e}rot (FP) cavity-enhanced configuration. This architecture leverages intracavity phase modulation to significantly steepen the transmission slope, boosting the FI by over two orders of magnitude compared to standard free-space configurations. This work provides a rigorous theoretical basis and design guidance for the high-precision quantum monitoring of electromagnetic environments in smart grids.